1. Field of the Invention
The present invention relates to repetitive control for causing a controlled object to conduct a repetitive action in response to a cyclic target input, and more particularly, to a discrete-type repetitive control method and an apparatus therefor, having an excellent response to a cyclic target input and excellent flexibility to a variation in the cycle period of a target input.
2. Description of the Related Art
Conventionally, it has been known to control a controlled object in a manner causing the object to repeat a single patterned action, by the use of a discrete-type repetitive control system which is constituted in accordance with an internal model principle and adapted to receive a cyclic target input which changes in a single changing pattern periodically repeated. According to the internal model principle, it is possible to cause an output of the controlled object to follow a target input with no steady deviation, by incorporating a target input generation model in a closed loop of the control system. Conventionally, in view of the internal model principle, a discrete-type repetitive control system has been so designed as to stabilize an extended system which is configured by connecting a compensator, including the target input generation model, to the controlled object.
In this case, a cyclic target input generation model represented by 1/(Z.sup.L -1) is employed, in view of equation (3) obtained by substituting equation (2) into a Z transform Yr(Z) of a cyclic target input y(t) represented by equation (1). In equations (1)-(3), symbols Z.sup.-1 (i=1, 2, - - - , L, 2L, - - - ) each represent a time delay element, and symbol L represents the cycle of the cyclic target input. ##EQU1##
Namely, as shown in FIG. 1, the conventional disorete-type repetitive control system accommodates therein an internal model 1/(Z.sup.L -1) which is comprised of L' time delay elements Z.sup.-1. The number L' of the time delay elements Z.sup.-1 is equal to a value obtained by dividing the cycle period L of the cyclic target input by a sampling cycle period .tau. of the cyclic target input in the control system. In FIG. 1, symbol yr(i) represents the cyclic target input; u(i), an input to the controlled object; and y(i), an output of the controlled object. Symbol x(i) indicates a state variable of the controlled object; and e(i), a deviation between the output y(i) of the controlled object and the cyclic target input yr(i). Further, symbol h represents a feedback gain element having a properly selected gain, and K1-KL indicate gain compensators having properly selected gains.
According to the repetitive control system, a stable control system is provided. However, if the state variable x (i) cannot be observed directly, then the repetitive control system shown in FIG. 1 cannot be configured. Further, according to the control system, the number L' of the time delay elements Z.sup.-1 must be equal to the value obtained by dividing the cycle L of the target input by the sampling cycle .tau.. Therefore, the conventional repetitive control system lacks flexibility to a variation in the cycle period of a target input.